Willingness-to-pay for financial aid

In Table4 below, we summarize the distributions of the estimated willingness-to-pay for the three types of financial aid packages (loans, grants and hybrid loans) of sizes $1,000 and $2,000.³⁰ Our results indicate that the median high school student would be willing to forego a $60.6 increase in current consumption to secure a $1,000 loan at the market interest rate in the near future. The willingness-to-pay for a $1,000 loan is highly heterogeneous across students, with an interdecile range equal to $174. While a quarter of the students are willing to sacrifice more than $116.7 for the option to take up a $1,000 loan, students in the bottom quartile are only willing to sacrifice less than $22.5.

As the experiment was conducted throughout the academic year, we can also examine how the willingness-to-pay for financial aid varies over time. In Table5 below, we document how the perceptions of credit constraints vary over time by reporting the distributions of the estimated willingness-to-pay for loans of sizes $1,000 and $2,000, separately for the students who were interviewed between October and December, and those interviewed between January and March.

28Since loan conditions were similar to those of the Federal Canadian Student Loan Program, such borrowing constraints may arise as some students exhaust their CSLP loan limits. In practice, over the year 2008-2009, a substantial share (37%) of the students who took up a federal loan reached the loan limit (Office of the Chief Actuary, 2009).

29In practice we setci=c³_i (background consumption level for the education financing questions).

30For the ease of exposition, we focus hereafter on financial aid packages of sizes $1,000 and $2,000. Estimation results for alternative amounts of financial aid are available from the authors upon request.

Table 4: The distribution of willingness-to-pay

$1,000 $2,000

Loan Grant Hybrid Loan Grant Hybrid

1st Dec. 4.6 68.3 71.3 5.1 160.9 140.9

1st Quart. 22.5 293.2 273.5 29.4 557.7 420.5 Median 60.6 449.8 409.0 72.2 792.4 578.5 3rd Quart. 116.7 638.8 566.0 129.7 1118.2 763.4 9th Dec. 178.6 795.0 682.1 182.3 1469.2 946.4 Notes: Amounts are in Canadian dollars.

Table 5: Willingness-to-pay for loans (time of the experiment)

Oct-Dec Jan-March

1,000 $ 2,000 $ 1,000 $ 2,000 $

1st Dec. 8.2 8.2 4.7 3.8

1st Quart. 29.1 36.5 22.0 27.4

Median 72.4 85.1 60.3 74.9

3rd Quart. 129.8 137.0 124.2 139.0 9th Dec. 192.7 197.7 178.7 196.2 Notes: Amounts are in Canadian dollars.

We find that students who are interviewed in the first half of the school year are generally willing to give up larger amounts of cash payments for the option to take up a college loan at the prevailing market rate. For instance, the median willingness-to-pay for a $1,000 ($ 2,000) loan is equal to

$72.4 ($85.1) among students who are interviewed between October and December, against $60.3 ($74.9) for those interviewed between January and March. Taken together, these results provide suggestive evidence that, as students learn about the financial aid opportunities during their senior year of high school, they tend to attach somewhat smaller values to the loans that are offered as part of the experiment. Importantly though, that the willingness-to-pay remains sizable among the students who are interviewed in the second half of the year indicates that imperfect information and learning about financial aid opportunities while in high school is not the only mechanism at play.

From a policy standpoint, a grant is equivalent to a tuition reduction, or a higher education subsidy. Not surprisingly, the value of a grant is typically much larger. The median student would be willing to trade in about $450 increase of their current consumption for the option to take up a

$1,000 grant. Contrary to loans, only a small share of the population attaches low values to grant

availability. For instance, less than 10% of the students would sacrifice $68 or less for a $1,000 grant, while more than half of them would do so for a $1,000 loan. That the vast majority of the students attach sizable values to grants is consistent with the fact that a very large share of them (93%) expect that they will enroll in a higher education institution (see Appendix G.1). More generally, for both amounts of financial aid ($1,000 and $2,000), the distribution of the willingness-to-pay for a grant stochastically dominates that of a loan.³¹

Turning to the hybrid packages, adding a loan to a grant generally has a small negative impact on the value of the package. This pattern holds true in most parts of the distributions of the willingness-to-pay. These results reflect the fact that, in practice, taking up a hybrid package entailed taking up both the loan and the grant components. It follows that those students who end up taking up the hybrid package upon college entry also have to pay the loan back with interest. As a result, how much students are willing to trade for a hybrid package versus a single grant depends on the incremental value of a loan, as well as on the interest cost associated with it. Our results indicate that, in this context, the latter effect dominates. At any rate, this provides additional evidence that our model fits the descriptive patterns previously reported in Section3 (Figures 1 and 2).

Finally, for loans, grants as well as hybrid loans, the value of the package generally increases with the size of the financial aid. Specifically, the distribution of the willingness-to-pay for a $2,000 loan (grant) stochastically dominates that of a $1,000 loan (grant), while a ($2,000 loan, $2,000 grant) hybrid loan also dominates that of a ($1,000 loan, $1,000 grant) hybrid loan. In particular, the results for loans provide suggestive evidence that, at least for a subset of the students in the sample, getting access to a $1,000 loan is not enough to remove higher education credit constraints.

One can quantify the magnitude of, and heterogeneity in credit market imperfections by converting the willingness-to-pay for any given loan into the interest rate wedge that students would be willing to pay on top of the prevailing (r₀= 5.7%) market interest rate in order to secure the option to take up that loan. Specifically, for a given loan of sizel and willingness-to-paycm, we define the effective interest rate as the interest rate, denoted by r₁(l, c_m), such that:

(1 +r1(l, cm)) (l−cm) = (1 +r0)l (10) The effective interest rate is defined as the interest rate associated with a total repayment (1 +r0)l(total repayment for a loanlat the prevailing market rate), and a principall−c_m(principal of the loanlnet of the willingness-to-pay for that loan).³² Note thatr₁(l, c_m), which is an increasing

31Both loans and grants might crowd-out parental transfers. Such a response would be captured in our estimates of the future value of, and willingness-to-pay for financial aid, provided that it is anticipated by the students at the time of the experiment.

32This definition abstracts from the fact thatcmis measured a few months before the loan is disbursed. Taking this lag into account when computing the effective interest rate - which would require additional assumptions in terms of timing and savings interest rate - would result in marginally larger interest rate wedges.

function of the willingness-to-pay c_m, is larger than the prevailing rater₀ for any positivec_m. We report in Table 6below the distribution of the interest rate wedges (r₁(l, c_m)−r₀) associated with a $1,000 loan and a $2,000 loan:

Table 6: The distribution of interest rate wedges (in percentage points) Quantiles $1,000 loan $2,000 loan

1st Dec. 0.49 0.27

1st Quart. 2.43 1.58

Median 6.82 3.96

3rd Quart. 14 7.33

9th Dec. 23 10.6

Note: Interest rate wedges are computed with respect to the prevailing market interest rate of 5.7%.

These results indicate that most of the students in our sample are willing to pay a sizable interest rate premium above the prevailing market rate for the option to take up a loan. The median interest rate premium students would be willing to pay is large and equal to 6.82 (3.96) percentage points for a $1,000 ($2,000) loan, respectively.³³ As expected given the results on the willingness-to-pay for loans documented earlier, the interest rate premia also exhibit much heterogeneity across students.

For the case of $1,000 loans, the interest wedge ranges from 0.49 to 23 percentage points for the first and the last decile, respectively. Overall, these results point to the existence of credit constraints, in the form of frictions in the market for college loans, which affect a substantial share of high school students in Canada. Our estimates further show that a non-negligible fraction of high school students attach pretty large values to the option to take up a college loan.

From a policy standpoint, these findings indicate that expanding higher education financial aid is likely be socially desirable in spite of the Canadian higher education system being already heavily subsidized. One potential avenue would be to increase the loan limits of the Federal Canadian Student Loan Program to accommodate a higher standard of living while in college. To the extent that the results from Table5above offer suggestive evidence that prospective students have imperfect information and learn while in high school about financial aid opportunities, it may also be desirable to develop an information campaign to accompany this type of policy.

To conclude, it is worth noting that, since some of the students in the sample expect not to enroll in college, our results effectively provide a lower bound on the willingness-to-pay for financial aid conditional on expecting to go to college. We address this issue by repeating our analysis on the

33It follows from Equation (10) that interest wedges are increasing with the willingness-to-paycm, but decreasing with the loan amountl. That the distribution of the interest wedges for a $1,000 loan dominates the distribution associated with a $2,000 loan is evidence that, in this context, the latter effect dominates.

subsample of students who declare that they expect (or aspire) to go to college.³⁴ The results are reported in TableA15in AppendixG.1. As expected, willingness-to-pay for financial aid tends to be larger for the students who expect (or aspire) to attend college. Expressed in terms of median interest rate wedges for a $1,000 loan, restricting to the group of students who expect (aspire) to go to college results in an increase from 6.8 to 8.2 (8.1) percentage points.